Most analytical models for the electrokinetic flow were developed for pipe or channel sizes sufficiently large or the zeta-potential sufficiently small for the application of Boltzmann distribution. With increasing interest in nano-fluidic flows, the effect of overlapping electrical double layer (EDL), which means that the pipe size is similar to or less than the Debye length, plays a more and more important role in the flow. The Boltzmann equation, which has been widely used to describe the ionic distribution in the EDL in the semi-infinite domain, is not applicable for the case of the overlapping EDL due to its limited flow space. The Nernst equation, instead, has been suggested in the literature.

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